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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 D + E + F = 0    (3)
-10B -8D + 2F = 40    (4)
 10A + 10B -4C = 20    (5)
 4C + 8D -8E = 20    (6)
Question solving process:

Multiply both sides of equation (1) by 10, the equation can be obtained:
         10A -10B -10F = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 D + E + F = 0    (3)
-10B -8D + 2F = 40    (4)
 20B -4C + 10F = 20    (5)
 4C + 8D -8E = 20    (6)

Multiply both sides of equation (2) by 10, the equation can be obtained:
         10B + 10C -10D = 0    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 D + E + F = 0    (3)
 10C -18D + 2F = 40    (4)
 20B -4C + 10F = 20    (5)
 4C + 8D -8E = 20    (6)

Multiply both sides of equation (2) by 20, the equation can be obtained:
         20B + 20C -20D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 D + E + F = 0    (3)
 10C -18D + 2F = 40    (4)
-24C + 20D + 10F = 20    (5)
 4C + 8D -8E = 20    (6)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
-24C + 20D + 10F = 20    (5)
 4C + 8D -8E = 20    (6)

Multiply both sides of equation (3) by 12
Divide the two sides of equation (3) by 5, the equation can be obtained:
         24C - 
216
5
D + 
24
5
F = 96    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
- 
116
5
D + 
74
5
F = 116    (5)
 4C + 8D -8E = 20    (6)

Multiply both sides of equation (3) by 2
Divide the two sides of equation (3) by 5, the equation can be obtained:
         4C - 
36
5
D + 
4
5
F = 16    (11)
, then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
- 
116
5
D + 
74
5
F = 116    (5)
 
76
5
D -8E - 
4
5
F = 4    (6)

Multiply both sides of equation (4) by 116
Divide the two sides of equation (4) by 5, the equation can be obtained:
         
116
5
D + 
116
5
E + 
116
5
F = 0    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
 
116
5
E + 38F = 116    (5)
 
76
5
D -8E - 
4
5
F = 4    (6)

Multiply both sides of equation (4) by 76
Divide the two sides of equation (4) by 5, the equation can be obtained:
         
76
5
D + 
76
5
E + 
76
5
F = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
 
116
5
E + 38F = 116    (5)
- 
116
5
E -16F = 4    (6)

Add both sides of equation (5) to both sides of equation (6) ,the equations are reduced to:
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
 
116
5
E + 38F = 116    (5)
 22F = 120    (6)

Multiply both sides of equation (6) by 19
Divide both sides of equation (6) by 11, get the equation：
         38F = 
2280
11
    (14)
, then subtract both sides of equation (14) from both sides of equation (5), get the equation：
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E + F = 0    (4)
 
116
5
E = - 
1004
11
    (5)
 22F = 120    (6)

Divide both sides of equation (6) by 22, get the equation：
         F = 
60
11
    (15)
, then subtract both sides of equation (15) from both sides of equation (4), get the equation：
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D + 2F = 40    (3)
 D + E = - 
60
11
    (4)
 
116
5
E = - 
1004
11
    (5)
 22F = 120    (6)

Divide both sides of equation (6) by 11, get the equation：
         2F = 
120
11
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 A -1B -1F = 0    (1)
 B + C -1D = 0    (2)
 10C -18D = 
320
11
    (3)
 D + E = - 
60
11
    (4)
 
116
5
E = - 
1004
11
    (5)
 22F = 120    (6)

Divide both sides of equation (6) by 22, get the equation：
         F = 
60
11
    (17)
, then add the two sides of equation (17) to both sides of equation (1), get the equation：
 A -1B = 
60
11
    (1)
 B + C -1D = 0    (2)
 10C -18D = 
320
11
    (3)
 D + E = - 
60
11
    (4)
 
116
5
E = - 
1004
11
    (5)
 22F = 120    (6)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 116, get the equation：
         E = - 
1255
319
    (18)
, then subtract both sides of equation (18) from both sides of equation (4), get the equation：
 A -1B = 
60
11
    (1)
 B + C -1D = 0    (2)
 10C -18D = 
320
11
    (3)
 D = - 
485
319
    (4)
 
116
5
E = - 
1004
11
    (5)
 F = 
60
11
    (6)

Multiply both sides of equation (4) by 18, get the equation：
         18D = - 
8730
319
    (19)
, then add the two sides of equation (19) to both sides of equation (3), get the equation：
 A -1B = 
60
11
    (1)
 B + C -1D = 0    (2)
 10C = 
50
29
    (3)
 D = - 
485
319
    (4)
 E = - 
1255
319
    (5)
 F = 
60
11
    (6)

Add both sides of equation (4) to both sides of equation (2), get the equation：
 A -1B = 
60
11
    (1)
 B + C = - 
485
319
    (2)
 10C = 
50
29
    (3)
 D = - 
485
319
    (4)
 E = - 
1255
319
    (5)
 F = 
60
11
    (6)

Divide both sides of equation (3) by 10, get the equation：
         C = 
5
29
    (20)
, then subtract both sides of equation (20) from both sides of equation (2), get the equation：
 A -1B = 
60
11
    (1)
 B = - 
540
319
    (2)
 10C = 
50
29
    (3)
 D = - 
485
319
    (4)
 E = - 
1255
319
    (5)
 F = 
60
11
    (6)

Add both sides of equation (2) to both sides of equation (1), get the equation：
 A = 
1200
319
    (1)
 B = - 
540
319
    (2)
 C = 
5
29
    (3)
 D = - 
485
319
    (4)
 E = - 
1255
319
    (5)
 F = 
60
11
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1200
319
    (1)
 B = - 
540
319
    (2)
 C = 
5
29
    (3)
 D = - 
485
319
    (4)
 E = - 
1255
319
    (5)
 F = 
60
11
    (6)


Therefore, the solution of the equation set is:
A = 
1200
319
B = - 
540
319
C = 
5
29
D = - 
485
319
E = - 
1255
319
F = 
60
11


Convert the solution of the equation set to decimals:
A = 3.761755
B = -1.692790
C = 0.172414
D = -1.520376
E = -3.934169
F = 5.454545

解方程组的详细方法请参阅：《多元一次方程组的解法》
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